Convergence of Nonlinear Recurrence Relations with Threshold Control and 2k− Periodic Coefficients

An nonlinear recurrence involving a piecewise constant McCullochPitts function and 2k−periodic coefficient sequences is investigated. It is found that each solution tends to h−1i or h1i, depending on whether the parameter λ varies from −∞ to +∞. We hope that our results will be useful in understanding interacting network models involving piecewise constant control functions.